Choose Calculator (n choose r)

Formula

The formula to calculate \(C(n, r)\) is:

\[ C(n, r) = \frac{n!}{r!(n-r)!} \]

Where:

\(C(n, r)\) is the number of combinations
\(n\) is an integer
\(r\) is an integer
\(!\) denotes factorial

Choose Definition

"Choose" is a term used in math to describe the operation of taking the combination of two numbers. It represents the number of ways to choose r elements from a set of n elements without regard to the order of selection.

Example Calculations

Example 1:

n = 5
r = 3

Using the formula:

\[ C(5, 3) = \frac{5!}{3!(5-3)!} = \frac{5!}{3! \cdot 2!} = \frac{120}{6 \cdot 2} = 10 \]

The number of combinations is 10.

Example 2:

n = 6
r = 2

Using the formula:

\[ C(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6!}{2! \cdot 4!} = \frac{720}{2 \cdot 24} = 15 \]

The number of combinations is 15.